Saxophonist Jesse Jones Jr. modeled his first band in high school, the Melt-Jess Jazz Quintet, after the muscular jazz of the Cannonball Adderley Quintet: Jones, of course, channeled Cannonball, the revered alto saxophonist and onetime Dillard High School teacher, and Jones’ younger brother, trumpeter Melton Mustafa, fancied himself Cannonball’s sibling, Nat.

The lifetime Miami-Dade resident hasn’t changed that arrangement much in the intervening half-century, still gigging in a band led by Mustafa, a recent survivor of Stage 4 prostate cancer, and taking the mixture of Southern sounds he collectively dubs “scat hop” — jazz, funk and soulful scatting rhythms on the mighty flute and sax — on solo shows to Germany and Russia.

“I never thought I’d get popular in Siberia,” admits the 67-year-old performer with a chuckle, speaking from his Miami Gardens home before heading off for a gig in Rockport, Mass. “I taught myself very young. My mom bought be a C-Melody sax for Christmas — I thought they were too poor — and she said, ‘That’s all you get. It’s on you now.’ “

Jones, who will double back to Delray Beach for a performance Saturday night at the Arts Garage, says he caught the sax bug at 9, when the brassy melody of his neighbor’s horn rattled the bedroom window of his Liberty City home. Influenced by his parents’ turntable collection of James Brown, the Marvelettes, the Temptations and, much later, his contemporary George Clinton (“Anything that had a funk to it, and was blues, we played it”), the charismatic sax man rode to early-career gigs with Mustafa in his father’s beat-up station wagon.

“I used to get on my brother so bad I would make him cry, because I wanted him to play trumpet so we would be like Cannonball band, and my mother would say, ‘Leave that boy alone!’ We started Melton with an E-flat horn,” he says. “Believe it or not, over the years, we’ve never had an argument. Ask anybody in my family.”

These days, Jones, who retired three years ago as a bailiff in the Miami-Dade court system, comes bounding onstage eager to lay down a flute solo for “Slo Blues,” one of his originals. For another original standby at live shows, “Com’n Home, Baby,” he delivers smoky blues vocals and promptly interrupts his singing with an abundance of scatting, including a low-pitched one and a falsetto variant that takes on the frequency of a chipmunk.

“I don’t consider myself a hell of a saxophone player, but it’s in my nature to throw everything at the audience. Even when I’m practicing, I’m moving and dancing around. My brother’s the same way. It’s in our genes,” Jones says. “I played in the Navy Band during Vietnam, and back then, I was a singer, a comic and a tap dancer. I can’t do a split now for nothing. You might as well call 911.”